JEE Advanced 2007 Paper 2Question 1
STATEMENT-1: The curve $y=\frac{-x^2}{2}+x+1$ is symmetric with respect to the line $x=1$.
because
STATEMENT-2: A parabola is symmetric about its axis.
Parabola
Solution
$y=-\frac{(x-1)^2}{2}+\frac32$ is a parabola with axis $x=1$, so $f(1+t)=f(1-t)$: Statement-1 is true. Statement-2 is true and is exactly the reason for Statement-1.